1. Presented by Nick Janus
LexRank: Graph-based Lexical Centrality as Salience in
Text Summarization
Presented by Nick Janus

2. Background Text summarization Intuitively, what sentences do we want?
Extractive summarization
Chooses subset of the original document's sentences
Better results
Abstractive summarization
Complicated - requires semantic inference and language generation
Often uses extractive summarization as a pre- processor
Intuitively, what sentences do we want?
This presentation is a mix of both!

3. Problem Statement Multi-document text summarization
Documents mostly share unknown topic
Cluster of documents represented by a network
Nodes in center are more salient to topic
How are edges defined?
How is centrality computed?
Topological clustering of documents is often noisy

4. Degree Centrality Top degree nodes are the most important
Cosine similarity is used to calculate edge weights:
A threshold is used to eliminate insignificant relationships
Use a bag of words model with N words
Each sentence/node is encoded as a N-dimensional vector - covariance matrix
Results in undirected graph

5. Degree Centrality Example
The threshold has a considerable impact on graph structure and ranking.

6. LexRank with threshold
So far, all nodes hold equal votes
More important sentences should have greater centrality (p()):
The vectors of each sentence form a stochastic matrix
To guarantee that the matrix converges to a stationary distribution, use a damping factor d, giving us PageRank:
For a graph to converge it must be irreducible and aperiodic

8. LexRank with threshold (cont.)
So how do we calculate LexRank? Algorithm redux:
Get the same cosine covariance matrix as before
Bin the values of the covariance matrix with the threshold
Regularize each value with neighbor degrees
Apply the power method so that the covariance matrix converges
The power method returns an eigenvector which contains the scores of all the sentences
where U is a square matrix with all elements being equal to 1/N. The transition kernel
[dU + (1 − d)B] of the resulting Markov chain is a mixture of two kernels U and B. A
random walker on this Markov chain chooses one of the adjacent states of the current state
with probability 1− d, or jumps to any state in the graph, including the current state, with
probability d.

9. Continuous LexRank What’s the problem with LexRank?
Discretizes node probabilities with a
Throws out information about sentences
Instead keep the data and use cosine similarity values, normalized to form a stochastic matrix:

10. Performance Baseline: Centroid-based summarizer Evaluation setting:
Compares sentences with a centroid meta-sentence containing high idf scoring words from document.
Evaluation setting:
Implemented with MEAD Summarization toolkit
Document Understanding Conference data sets
Model summaries and document clusters
Rouge metric
Measures unigram co-occurence

12. curated sets
DUC Data Sets

13. 17% noisy
Noisy Data Sets

14. Summing Up
Centrality methods may be more resilient in the when dealing with noisy document sets
Multi-document case
Difficult evaluation
Better performance
Relation to PageRank